Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
Correct Answer
$6897
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5700 × 3% × 7
= $5700 ×3/100 × 7
= 5700 × 3 × 7/100
= 17100 × 7/100
= 119700/100
= $1197
Thus, Simple Interest = $1197
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1197
= $6897
Thus, Amount to be paid = $6897 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5700
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 3% × 7)
= $5700 + ($5700 ×3/100 × 7)
= $5700 + (5700 × 3 × 7/100)
= $5700 + (17100 × 7/100)
= $5700 + (119700/100)
= $5700 + $1197 = $6897
Thus, Amount (A) to be paid = $6897 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5700, the simple interest in 1 year
= 3/100 × 5700
= 3 × 5700/100
= 17100/100 = $171
Thus, simple interest for 1 year = $171
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $171 × 7 = $1197
Thus, Simple Interest (SI) = $1197
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $1197
= $6897
Thus, Amount to be paid = $6897 Answer
Similar Questions
(1) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?
(9) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.